Li₂FePO₄F and its metal-doping for Li-ion batteries: an ab initio study

Abstract

The electrochemical properties of three isotopic Li₂FePO₄F compounds, as cathode materials under different space groups Pbcn, P1̄ and Pnma were investigated using first principle calculations. Their structures and average open circuit voltages for step delithiation reactions were explored, and the results are in good agreement with the reported experimental data. We estimate the substitution effect of Fe by Co in Pnma-Li₂FePO₄F. The substitution of Fe by Co in Li₂Fe_1−xCo_xPO₄F may enhance the discharge potential of the materials, and the rate of its volume change during the redox process is between 0.6% and 2.1%. Furthermore, from the projected density of states for Li₂Fe_0.5Co_0.5PO₄F, we found strong hybridization for Fe-3d and Co-3d bands near the Fermi level, which implies that the Co-doped Li₂Fe_1−xCo_xPO₄F may possess better electronic conductivity than the pure phase.

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1 Introduction

Commercialized lithium ion batteries (LIBs) have rapidly penetrated into everyday life since Sony announced the first version in 1992.^1–6 Important battery performance characteristics are mainly determined by the electrochemical properties of the electrode materials, especially the cathode. The conventional positive materials for LIB such as LiCoO₂, Li₂MnO₃ and LiFePO₄ have been widely studied and optimized.^7,8 For example, LiFePO₄ is the most prominent compound in the transition metal polyanionic family,^9,10 and its major limitations are the poor electrical conductivity and the one-dimensional Li-ion diffusion. Its relatively poor electronic conductivity can be more than offset by decreasing the size of crystallite,¹¹ doping transition metal¹² and coating conductive additives onto the surface.¹³ However these strategies increased the complexity and reduced the reliability of the material's manufacture, hence it is desirable to develop new polyanion-type cathode materials for lithium ion batteries. Yang et al. had reported a detailed description for this families,¹⁴ one of the most interesting poly-anion compounds is that of fluorophosphates. A₂MPO₄F materials (A = Na, Li; M = Fe, Mn, Co, Ni, etc.) have been proposed as promising candidates for high-energy-cathode materials, especially for A = Li.^15–23

The Li₂MPO₄F family has attracted much attention for the following reasons: firstly, fluorophosphates compounds exhibit high specific capacity and energy density, when the exchange of more than one alkali atom per formula unit (f.u.) was considered. Secondly, it possesses facile two-dimensional pathways for Li⁺ transportation and the structure changes on redox are relatively small.^17,20 Additionally, the high electronegativity of F⁻ serves to increase the thermal stability of Li₂MPO₄F compared to LiMPO₄.¹⁷ Four space groups for Li₂MPO₄F have been widely investigated experimentally: Pnma (M = Fe, Ni, Co),^18,19,21 Pbcn (M = Fe),¹⁷ P1̄ (M = Fe),^20,24 P2₁/n (M = Mn).^16,22 Accordingly, Li₂FePO₄F could adopt both tetragonal and triclinic structures, which depends on synthetic procedures.^17,20–22 The synthesis of Li₂FePO₄F remains difficult and requires either the ion exchange of the Na₂FePO₄F/LiNaFePO₄F or a lengthy solid state reaction.^17,20,21 One appealing strategy for improving the cathode properties is to develop mixed transition metal compounds,^25–28 this approach has been widely applied to other material families. The influence of metal-doping on the performance of a cathode material for LIB has been investigated from both theoretical and experimental aspects.^12,29–31 Nevertheless, to the best of our knowledge, the metal-doping for Li₂FePO₄F has not yet been reported. High-throughput density functional theory calculations had been explored and made enormous contribution to the LIB field in predicting the structural behavior and electrochemical properties. To individuate the most promising candidates for practical applications and optimize Pnma-Li₂FePO₄F, we investigated the electrochemical and electronic properties by metal-doping (M = Co) using ab initio methods.

Herein we systematically investigated the influence of crystal structure and relative stability on the electrochemical properties of Li₂FePO₄F polymorphs as cathode materials for LIB. A comparative study of three reported polymorphs crystallized of Li₂FePO₄F (with space groups Pbcn, P1̄, Pnma) was also performed. Our computed structures, average open circuit voltages of Li₂FePO₄F are in good agreement with the experimental data. The calculated results revealed that Pnma-Li₂FePO₄F possesses the highest electron conductivity among investigated space groups. We explored the structure, electrochemical stability and projected density of states (PDOS) of substitution of Fe by various degree levels of Co using first principle computations as a screening tool.

2 Computational methods

All the calculations were performed by using ab inito methods implemented in the Vienna Ab Initio simulation package (VASP),^32–35 which is based on the density functional theory (DFT). Generalized-gradient approximation (GGA) with the functional of Perdew, Burke and Ernzerhof (PBE) was used to describe the potential. Projector augmented wave (PAW) was employed to describe the electron wave functions.³⁶ PAW method has been widely used for battery materials and shown excellent predictive capability.^37–39 The GGA + U method was used to accurately calculate structural and electronic properties, because of the strong localization of the 3d orbital such as phosphate materials, incomplete cancellation of the self-interaction of the GGA is often reported to cause large errors.⁴⁰ We used the effective U parameter for transition metals (TM), U_Fe = 4.5 eV,⁴¹ U_Mn = 4.5 eV,⁴¹ and U_Co = 3.4 eV,⁴² respectively. A planewave cutoff energy of 400 eV was used for all computations, and appropriate k-points meshes were chosen to ensure that the total energies were converged within 2 meV per f.u. Gaussian smearing was used with a smearing parameter of 0.20 eV. The calculated energy difference between ferromagnetic (FM) and antiferromagnetic (AFM) ordering was less than 6.5 meV per f.u., implying that the magnetic structure has less effect on the energy calculations. Thus the calculations were performed in a high-spin ferromagnetic ordering. Initial magnetic moments were set to high-spin for Mn, Fe, and Co and low-spin for other elements.⁴³

The initial atomic positions for Li₂FePO₄F were taken from ref. 20 (P1̄), ref. 17 (Pbcn), ref. 21 (Pnma), and the two Li ions were removed from the Li₂FePO₄F polymorphs to generate FePO₄F. For the intermediate LiFePO₄F, the Li-vacancy arrangements were taken from the ref. 17, 20 and 21 for Pbcn, Pnma and P1̄, respectively. For metal-doping calculations, all structures were fully relaxed (cell parameters, cell volume, and atomic positions), and performed in an 8-f.u. Li₂FePO₄F supercell, in which 1–8 Fe atoms were replaced one by one by Co atom, respectively. The migration energy barriers for diffusion of Li atom are calculated by the Cl-NEB method.⁴⁴

Ab initio methods have been widely used to predict the average voltages of lithium deintercalation/intercalation in many compounds.^45,46 Following the well-established methods, the open circuit voltage (OCV) V vs. Li/Li⁺ can be calculated from the energy difference, if volume and entropy effects are neglected:⁷

3 Results and discussion

3.1 Cell parameters, energy and structural characteristics of Li₂FePO₄F polymorphs

In this work, three Li₂FePO₄F polymorphs with the space groups of Pbcn, P1̄ and Pnma are considered. Their optimized lattice parameters, volumes changes and average voltages are listed in Table 1, together with the available experimental results. For the three polymorphs of Li₂FePO₄F, the calculated lattice parameters are in good accordance with the experimental data, for example, the discrepancies between calculated and experimental volumes of the unit cell are lower than 2.55%. Noting that our calculated results for Pbcn-Li₂FePO₄F polymorph are consistent with the previous report.⁴⁷

Table 1 The optimized lattice parameters, specific capacities, volume changes, and average voltages for Li₂FePO₄F of Pbcn, P1̄, and Pnma space groups, compared with available results

Li2FePO4F	Pbcn			P1̄		Pnma
Lattice parameter	Calc	Exp^a	Ref^b	Calc	Exp^c	Calc	Exp^d
a From ref. 17.b From ref. 46.c From ref. 20.d From ref. 21.
a (Å)	4.99	5.05	4.95	5.34	5.37	10.61	10.78
b (Å)	13.07	13.56	13.09	7.35	7.48	6.33	6.27
c (Å)	11.37	11.05	11.17	5.35	5.33	11.13	11.03
V (Å^3)	742.06	723.60	757.62	184.64	189.14	746.8	744.5
Volume discrepancies	2.55%			2.34%		0.31%
Fe^3+/Fe^2+ (V)	3.27	3.50		2.43	2.75	3.50	3.40
Fe^4+/Fe^3+ (V)	5.20			5.09		5.02

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We also compared the electrochemical properties of three compounds, the average deintercalation voltage for the first and second Li⁺ are show in Table 1. In P1̄-Li₂FePO₄F, Fe³⁺ → Fe²⁺ redox couple is at 2.7 V vs. Li/Li⁺, about 0.7 V lower than the same redox transition in Pbcn-Li₂FePO₄F and Pnma-Li₂FePO₄F. For all the polymorphs, the oxidation of Fe³⁺ to Fe⁴⁺ occurs at a very high voltage (∼5.1 V), which makes it necessary to use an electrolyte with a wide electrochemical window, like ionic liquids. Fig. 1 shows the calculated total energy as a function of volume obtained from the Li_yFePO₄F (y = 2, 1, 0). For Li₂FePO₄F, the total energy differences between Pbcn and Pnma-Li₂FePO₄F polymorphs are very small at 0 K, this phenomenon explains why synthesis of Li₂FePO₄F need to use ion exchange of the Na-counterparts,^17,21 while for synthesized directly may easily result in a mixture of Pbcn and Pnma-Li₂FePO₄F. And the total energy of Pbcn and Pnma-Li₂FePO₄F is lower than P1̄-Li₂FePO₄F, hence P1̄-Li₂FePO₄F was less stable than Pbcn and Pnma. We stress that tavorite-type structure of P1̄-Li₂FePO₄F prepared by reduction of LiFePO₄F differs greatly from ion-exchange of the Na-counterparts.²⁰

Fig. 1 Calculated total energy vs. volume curves for Pbcn, P1̄ and Pnma polymorphs of Li_yFePO₄F (y = 2, 1, 0).

From Fig. 1, it can be observed that the unit cell volume contracts during the first and second delithiation step for both P1̄ and Pnma-Li₂FePO₄F, however the unit cell volume increases for Pbcn-Li₂FePO₄F when it is fully delithiated to form FePO₄F, this phenomena is correlated with d–p mixing.⁴¹

In Fig. 2, all Li₂FePO₄F polymorphs are built of FeO₄F₂ octahedra and PO₄ tetrahedra, and each Fe atom is surrounded by two fluorine atoms and four oxygen atoms. The connectivity of the octahedral varies from the layered structure to the 3D structure.

Fig. 2 The optimized crystal structures of three Li₂FePO₄F polymorphs. Pbcn: ((a) and (b)) view along the b and c axis, respectively; P1̄: (c) view along the c axis; Pnma: (d–f) represent the direction of [100], [011], [010], respectively. Violet octahedra, turquoise tetrahedra, and gray balls represent FeO₄F₂, PO₄ and Li⁺, respectively.

Fig. 2a and b show the orthorhombic structure of Pbcn-Li₂FePO₄F with the layered structural features including pairs of face-sharing metal octahedra, two alkali-ions locate in the interlayer space, and two-dimensional pathways for Li⁺ transport.¹⁷ In the triclinic P1̄ tavorite-type framework (Fig. 2c), the FeF₂O₄ octahedra forms corner-sharing 1D chain in the b axis with alternating tilted octahedral bridged by the F⁻ ions, and these chains are connected by corner-sharing the phosphate tetrahedra to create a spacious 3D structure. For the Pnma-Li₂FePO₄F (Fig. 2d–f), the structure consists of edge-sharing chains of FeF₂O₄ octahedra running along the b axis, and the channels along the [011] and [010] are capable of Li⁺ diffusion.

Nellie et al. also showed experimentally that the Pnma-Li₂FePO₄F with a 3D framework exhibits several advantages over other iron-based fluorophosphates, for instance, the volume change upon redox is one quarter of P1̄-Li₂FePO₄F and a half of Pbcn-Li₂FePO₄F.²¹

3.2 Factor-Q for three Li₂FePO₄F polymorphs

The search for a general quality criterion addressing the potential of three polymorphs of Li₂FePO₄F as cathode materials should be taken fully into account both the OCV and band gaps (BG) values. A material with a high electrochemical potential which make it an attractive candidate for cathodes used in high-energy batteries. The high OCV corresponds to a high electrochemical potential, while the low BG corresponds to high electronic conductivity of material. Mustarelli et al. raise the Quality factor, Q,²⁵ which is proposed by combining the above-mentioned observables:

Q = OCV/BG

We calculated total density of states of Li₂FePO₄F/LiFePO₄F (see ESI Fig. S1†), the BG are determined from the calculated density of states and listed in Table 2. It is shown that both Li₂FePO₄F and LiFePO₄F, the lowest BG values are obtained in the frame of the Pnma space group.

Table 2 The values of band gaps for Li₂FePO₄F and LiFePO₄F with three space groups

Space group	BG (Li2FePO4F)/eV	BG (LiFePO4F)/eV
Pnma	3.196	1.301
Pbcn	3.465	2.578
P1̄	3.639	2.539

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The calculated behaviors of the Q for Li₂FePO₄F and LiFePO₄F with three space groups are presented in Fig. 3. Q values were increased from lithiated states (Purple) to delithiated (dark yellow) states of LiFePO₄F. Compared with Pbcn and P1̄ Li₂FePO₄F/LiFePO₄F polymorphs, Pnma-Li₂FePO₄F/LiFePO₄F may be the best cathode material with the largest Q values.

Fig. 3 The behaviors of the Q for Li₂FePO₄F and LiFePO₄F with three space groups.

3.3 Co-doped Pnma-Li₂FePO₄F

It is well known that the Co²⁺/Co³⁺ has a relatively high redox voltage. For example, fluoride phosphate Li₂CoPO₄F (ref. 19, 48 and 49) possesses the highest redox potential among available cathodes currently (5.1 V vs. Li/Li⁺). It can be expected that the substitution of Co for Fe at Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) may increase the discharge potential (i.e. energy density) of the materials. Moreover, Pnma-Li₂CoPO₄F is isostructural with Pnma-Li₂FePO₄F, hence Co-doped Pnma-Li₂FePO₄F, i.e. Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1), may not occur a phase transformation like Na₂Fe_1−xMn_xPO₄F.⁵⁰ Previous report revealed that the Li₂MnPO₄F belongs to the P2₁/n space group,¹⁶ for comparison, we investigate the stability of the Co/Mn-doped Pnma-Li₂FePO₄F as well (see detail in the ESI†). The calculated results suggest that Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) is stable enough as a new cathode material, but Li₂Fe_1−xMn_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) might easily decomposed into LiMnPO₄, LiFePO₄ and LiF (as illustrated in Fig. S2 in ESI†). This can be traced back to the isostructural of Li₂CoPO₄F with Pnma-Li₂FePO₄F, while Li₂MnPO₄F is different. Hereafter, we estimate the structure, electrochemical properties and PDOS of Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1) in the following calculations.

3.3.1 The lattice parameters of Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8). The lattice parameters and unit cell volume for Li₂Fe_1−xCo_xPO₄F (0 < x < 1) are summarized in Fig. 4. The a and b lattice parameters almost remain the same upon the substitution of Fe by Co, while c values are decreased. As a result, the unit cell volume of Li₂Fe_1−xCo_xPO₄F should decrease with the substitution of Co for Fe, because of the ionic radius Fe^II > Co^II (Co^II: 0.745 Å, Fe^II: 0.780 Å for high-spin state within six-fold coordination).⁵¹ To evaluate the affect of decrease volume to the Li conductivity in the materials, we also calculated the activation barriers of Li₂Fe_1−xCo_xPO₄F (x = 0, 0.25, 0.75) in the ESI (Fig. S5†). It is found that the higher doping concentration leads to higher migration barriers for diffusion of Li.

Fig. 4 The unit cell parameters and volumes for different compounds of Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8).

3.3.2 Most probable doping model. There are two distinct positions for Fe, namely Fe₍₁₎ (4a sites) and Fe₍₂₎ (4b sites) in Pnma-Li₂FePO₄F structure though they have same coordination environments (ESI, Fig. S3†). From Table 3, it is clear that the Fe–X distances and the O–Fe–O/F angles are different for Fe₍₁₎O₄F₂ and Fe₍₂₎O₄F₂ octahedra. The distance of Fe₍₁₎–O (2.08 Å) and Fe₍₂₎–O (2.05 Å) are similar, while the average bond length of Fe₍₂₎–F is ∼0.1 Å longer than that of Fe₍₁₎–F. The increasing of Fe–F distance may cause the decrement of static electricity, and Co may be inclined to substitute for Fe₍₂₎ (4b sites) atom. Pnma-Li₂FePO₄F has some distortion in the Fe₍₁₎O₄F₂ and Fe₍₂₎O₄F₂ octahedra, which may reduce the structural stability. For instant, the higher distortion of angles of O–Fe₍₁₎–O/F than those of O–Fe₍₂₎–O/F may results in the higher instability of Fe₍₁₎O₄F₂ octahedra structure.

Table 3 Optimized Fe–O/F average lengths and angles of O–Fe–O/F

Bonds	Average Length (Å)	Angle	Value (°)
Fe(1)–O	2.08	O–Fe(1)–O	84.99
Fe(2)–O	2.05	O–Fe(2)–O	85.61
Fe(1)–F	2.13	O–Fe(1)–F	101.42
Fe(2)–F	2.22	O–Fe(2)–F	97.94

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We calculated the energies of 23 configurations for Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1), in the Pnma host, using the supercells up to 8-f.u. (Li₁₆Fe₈P₈O₃₂F₈). In Fig. 5, we displayed the total energies (in black) and unit cell volume (in red) for most stable substituted Li₂Fe_1−xCo_xPO₄F (0 < x < 1), where the labels (1) and (2) refer to positions of Fe.

Fig. 5 The calculated energies and unit cell volume for Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8).

From Fig. 5, it is evident that the substitution of Co for Fe₍₂₎ at Li₂Fe_1−xCo_xPO₄F possesses lower energy values than Fe₍₁₎. Consequently, Fe₍₂₎ may be more favorable in the Co substitution than Fe₍₁₎. When x = 0.375, the energy for 222 site is only 0.85 meV per f.u. higher than that of 221 site, nevertheless, such a small value is at the range of error limitation. For the different concentrations of 12.5%, 25%, 37.5%, the trend is that the most stable multicomponent fluorophosphates compounds (with lower total energy) have the largest volume. However, no direct correlation between the volume and the total energy were observed at other concentrations. We also calculated the energies of vacancies of Fe₍₁₎ and Fe₍₂₎, and the results show that Fe₍₂₎ vacancy has lower total energy, consequently, Co may substitute the Fe atom at the Fe₍₂₎ site preferentially.

3.3.3 OCV. It is instructive to investigate the electrochemical parameter OCV, which usually contains enough information to decide whether a material is of interest as a cathode candidate for Li-ion batteries.⁴¹ Fig. 6 shows the two voltages corresponding to the extraction of two Li ions in two consecutive electron redox processes. These results also confirmed our former prediction that the substitution of Co for Fe at Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) can increase the discharge potential of the material. Interestingly, the first voltage step (y from 2 to 1) increases 0.1 V, when the concentration of Co increases by 12.5%, while the fully delithiated voltage step (y from 1 to 0) increases by about 0.02 V with the substitution of Co for Fe. The volume changes of Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) upon redox are in the range of 0.6–2.1% (see ESI, Fig. S4†), which is smaller than that of LiFePO₄ (6.7%), indicating that Li₂Fe_1−xCo_xPO₄F is stable enough to be new cathode materials.

Fig. 6 The calculated total energy for Li_yFe_1−xCo_xPO₄F in the lithiated (y = 2), semi-delithiated phase (y = 1) and full-delithiated phase (y = 0) together with the calculated cell voltages.

3.3.4 Electronic structure of Li₂Fe_1−xCo_xPO₄F. To evaluate the electron properties we calculated the electronic structure of Li₂Fe_1−xCo_xPO₄F. Fig. 7 shows the PDOS onto the d-orbital of the TM of the Li₂Fe_1−xCo_xPO₄F (x = 0.25, 0.375, 0.5, 0.75). Only electron states near the Fermi level play the key role in the electron transport processes, thus we mainly focus on the PDOS around the Fermi energy. Careful inspection of Fig. 7 demonstrates that there are two parts in the DOS patterns around the Fermi level those are un-completely filled 3d orbitals of transition metal located below the Fermi level, and empty 3d orbitals located above the Fermi level.²⁵ For Li₂Fe_0.75Co_0.25PO₄F that is x = 0.25 both valence and conduction states are mainly contributed from Fe 3d orbitals. When x = 0.375 the conduction bands localized about 3.0 eV are mainly due to Co-3d states and this configuration leads to a lower BG, while for x = 0.75, the energy region just above Fermi level dominated by unoccupied Co 3d orbitals. It is interesting to note that at the concentration of 50%, i.e. Li₂Fe_0.5Co_0.5PO₄F, the occupied Co-3d states are strongly hybridized with the Fe-3d states near the Fermi level. The Li₂Fe_1−xCo_xPO₄F can be considered as semiconductor at the Co concentration of x = 0.25, 0.375, and 0.75; while this material shows metallic at x = 0.5. To investigate the difference electronic properties of Li₂Fe_1−xCo_xPO₄F (x = 0.25, 0.5, 0.75), we plotted the electron localization function (ELF) in the ESI (see Fig. S6†). Thereby with the increasing of Co doping content, the contribution of 3d orbital of cobalt to the TDOS around the Fermi level is increases correspondingly. Thus, the Co-doped Li₂FePO₄F may have better electronic conductivity than the pure phase.

Fig. 7 The calculated PDOS of Li₂Fe_1−xCo_xPO₄F (x = 0.25, 0.375, 0.5, 0.75), PDOS for different atoms are denoted by different colors to indicate their contribution.

4 Conclusion

We have investigated the Pbcn, P1̄ and Pnma space groups of Li₂FePO₄F by using first-principle DFT computations. The calculated average intercalation voltages, as well as the lattice parameters, agree well with available experimental results. In particular, Pnma-Li₂FePO₄F is interesting as far as the electron conductivity is concerned. For transition metal doped Pnma-Li₂FePO₄F, Li₂Fe_1−xCo_xPO₄F may be stable enough to be used as new cathode materials. Furthermore, the substitution of Co for Fe i.e. Li₂Fe_1−xCo_xPO₄F (0 < x < 1) favors to increase the discharge potential of the pure materials, although the migration barriers for diffusion of Li are increased to some extent as well. The small volume change (0.6–2.1%) on the removal of one or two Li⁺ per f.u., suggests that Li₂Fe_1−xCo_xPO₄F (x = 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8) is stable enough to be utilized in the cathode materials. The PDOS of Li₂Fe_0.5Co_0.5PO₄F shows both Co-3d and Fe-3d states contributing to the electronic states around the Fermi level, indicating it may possess better electronic conductivity than the Pnma-Li₂FePO₄F.

Acknowledgements

Financial support by the NSFC (21173037 and 21274017) is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available: (S1) The total DOS of Li₂FePO₄F and LiFePO₄F. (S2) The stability of Li₂Fe_1−xM_xPO₄F (M = Co, Mn). (S3) Positions of Fe in Pnma-Li₂FePO₄F. (S4) Volume changes of Li₂Fe_1−xCo_xPO₄F upon delithiation. (S5) Migration barriers for diffusion of Li atom in Li₂Fe_1−xCo_xPO₄F. (S6) The electron localization function (ELF) of Li₂Fe_1−xCo_xPO₄F (x = 0.25, 0.5, 0.75). See DOI: 10.1039/c4ra06170e

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